On Uncertainty (Part 1)

This post is a part of a two part series I am going to do. It's been almost a month since my last update! A lot of things have happened since then, but this post - I really want to focus on something that has been tying all of my experiences the past month together - uncertainty.

The relevant Rebel Without a Cause quote here : "I firmly believe in the laws of probability."

My dad never really wanted to study engineering - he said he always wanted to study economics and statistics, but unfortunately never got the chance.

When I was younger, I hated statistics - especially probability and combinatorics. It never made sense to me - how many ways can you put 5 letters incorrectly in 5 envelopes, or what's the probability of drawing a two hearts in 5 cards, etc? The solutions required long methods, and more often than not, clever thinking and counting tricks. I never liked doing mathematics when I was younger, and doing these kind of statistical problems was just prolonging the painful experience!

But today, practically all I'm doing in some form is related to statistics. In my machine learning theory class, we are proving why algorithms work through a hardcore statistical framework. My chemistry classes were underpinned by the Born interpretation of quantum mechanics, and chemical engineering was underpinned by the statistical interpretation of macro-thermodynamics of systems. I think the point being, is that fundamentally, statistics give a measure of uncertainty, a powerful tool at best to give us some confidence in an uncertain world - but going philosophically, I don't think it gives us meaning though, just the overall inflexible idea.

Case in Point:

A law of probability that we have often used in statistics is the Hoeffding's Theorem which states that the the difference between an average of a group of random variables and the true value of the mean of the random variable is bounded by a exponential function of the bounds of the random variable (b, and a). In other words, the true value and the sampled value only differ by some constant epsilon with great certainty, and the probability is bounded.

Now the reason, I brought this up is because I want to give a toy example using this theorem - say a human life max life expectancy is 120 years, so that is our bound. Now no one really knows how long a person is going to live, but this theorem gives us a probability bound of how much longer can they live then their real life expectancy. Think about it as how confident can I be in prolonging my life.

Using this theorem, if a human life is to end somewhere between 0 and 120 years, we find that with 50% chance, the human life can outlive its own death by 70 years. What a crazy fact - that a coin toss is sufficient to tell us if we can outlive our true death day another 70 years, and we only needed the max life expectancy of a human to tell us that.

But that doesn't give us any comfort or meaning whatsoever - 70 years is a long time. What the hell are we going to do for 70 years, if we are that lucky? It doesn't give any answers - just a cold hard number without any regard for much else - the law of probability is just there.

How do I interpret this fact?

The past month offers two points for me - I took my PE Chemical exam on February 2nd, after 3 weeks of studying, and a weekend of doing practice problems. In all words, I was not at all ready - the exam is designed to be taken by professionals who have had at least 2-4 years of engineering experience and many of the questions in the exam reflected the fact of needing actual field experience to answer.

My first thought when I saw the first question - I should've started studying way earlier!

When I finished the exam, I honestly had no idea - I felt that I had a 50-50 percent chance either way of passing or failing, or I messed up so bad that there is no chance. I couldn't really sleep for the following week, as the results come out after a week. On February 10th, I found this:

which to me was a huge surprise - a pleasant one at least! But it really got me thinking, this didn't really do anything in the grand scheme of things - life just went on - exams were still happening, homework was due, and research was still up.

However, in the smallest scheme of things, it changed a couple of things - I am more confident in pushing out my ideas related to engineering and my PI and colleagues have more confidence in me as hard-worker

My motivation of taking the PE exam came from my mother. I remember her studying for the much much tougher PE Civil exam when I was 12, putting late nights in, driving to Texas herself to take the exam, and how proud and happy she was when she passed. I remember telling my teachers yeah, my mom has a doctorate and a professional engineer's license, and they would be really amazed.

My initial thoughts was that I wanted to feel that same sense of accomplishment my mom did, but now almost 3 weeks later, it just made me more proud of my mom for who she is. She really gave meaning to me when I decided that I wanted to follow her landmark footsteps to become a professor.

See when I studied for the exam, I wasn't battling the same uncertainty my mom did. No one in our family had a PE license, no other female professor in her department where she taught had a PE license, and furthermore, she did it while still taking care of me while my dad was in India fixing an impossible problem (another post!). She managed to tough the entirety of it out, and I realised that bullshit approach which I took, was only possible because I saw my mom pass the exam.

In a way, having and seeing my mom fight the uncertainty before I had to from doing a doctorate to passing her PE, gives me untold confidence that I can and will finish my PhD and get into academia.

Going back to the laws of probability, it just goes to show that the grand scheme of things are always determined, there's nothing I can do to change it - but the smallest things are the ones that end up bringing meaning and end up changing the individual.

Part 2: Coming on Wednesday!